IMPLICATION AND FUNCTIONAL DEPENDENCY IN INTENSIONAL CONTEXTS

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Abstract

Formal concept analysis is a mathematical field applied to data mining. Usually, a formal concept is defined as a pair of sets, called extents and intents, for a given formal context in binary relation. In this paper we review the idea that Armstrong’s inference rules are complete and sound for functional dependencies. Then, we prove that Armstrong’s inference rules are complete and sound for implications of formal contexts. Still, we give an example which shows the difference between implication and functional dependency. Besides, we show that functional dependency can be reduced to implication. Finally, we give the condition on which a set of implications and a set of functional dependencies for the intensional context are equivalent.

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